1. Field of the Invention
This invention relates to radar imaging airborne weapons, and more particularly to super-resolution radar imaging of range-to-target and angle-to-target during the weapon's terminal phase or endgame.
2. Description of the Related Art
A radar imaging airborne weapon such as a missile, smart projectile etc. engaging a target is expected to move through a phase where high-resolution imagery such as synthetic aperture radar imaging is used to detect, identify, and classify ground targets. A particular target of interest will then become the chosen destination of the weapon. In an air-to-air encounter, a target at far range is treated as a point source target in the acquisition and midcourse guidance portion of flyout. In both cases, individual scatterers on the target begin to resolve as the weapon closes to within a few kilometers of the target, thus requiring imaging and angle exploitation techniques that can handle multiple scatterers.
At the beginning of the imaging stage, the weapon has a velocity vector that is not pointed directly at the scene of interest (i.e. it is flying a squinted trajectory). The angle between the velocity vector and the region of interest is generally 10-20 degrees depending on velocity, frequency, and resolution requirements. This imaging step can be expected to last until about 1.5-3 kilometers away from the target. Once this distance of 1.5-3 kilometers is reached, the weapon will begin what is commonly referred to as endgame or terminal phase. The weapon will turn toward the target to engage it. At this point, with the velocity vector pointing almost directly at the target of interest (zero squint), the weapon's radar suffers a loss in cross-range resolution due to its small physical antenna aperture and approximate co-alignment of range and Doppler contours. Despite this loss in resolution, the weapon must maintain a precise aimpoint to the target of interest or risk missing its objective. Aimpoint selection is further complicated by the fact that the endgame geometry changes rapidly (e.g., the target rapidly fills the antenna beam as the weapon approaches at a high rate of speed).
Another challenge encountered in the terminal phase of detection and localization of ground targets is that clutter may be folded into the target. The signal to noise (SNR) ratio is greatly increasing as range decreases, but clutter power increases also. As a result, the ability to directly detect the target becomes extremely difficult as the squint goes to zero and the target begins to fill the entire radar beam. Another problem that is encountered in both air-to-air and air-to-ground scenarios is the phenomenon of glint. As the weapon rapidly approaches the target, the coherent sum of the target's dominant scatterers changes rapidly, which can cause wide apparent variations in the target's aimpoint when using techniques such as monopulse.
Geometry greatly impacts the processing required to find an accurate aimpoint. The geometry of interest consists of a forward-looking antenna beam pattern that is directed in the same direction as the velocity vector of the weapon (zero squint). This geometry results in Doppler resolution cells that are larger than the beamwidth of the antenna. This is because the Doppler shifts of scatterers at the edges of the beam are nearly identical to the Doppler shifts of scatterers at the center of the beam. For example, consider a Ka-band radar traveling at 300 m/s directly along its line-of-sight vector. For an antenna beamwidth of 3 degrees, the Doppler shift of one side of the beam relative to the center of the beam is:
                              Δ          ⁢                                          ⁢                      f            D                          =                                                            2                ⁢                                                                                              v                      _                                        radar                                                                                λ                        ⁡                          [                                                cos                  ⁡                                      (                                          0                      ⁢                      °                                        )                                                  -                                  cos                  ⁡                                      (                                          1.5                      ⁢                      °                                        )                                                              ]                                =                                                                      2                  ·                  300                                .0086                            ⁡                              [                                                      cos                    ⁡                                          (                                              0                        ⁢                        °                                            )                                                        -                                      cos                    ⁡                                          (                                              1.5                        ⁢                        °                                            )                                                                      ]                                      =                          24              ⁢                                                          ⁢              Hz                                                          (        1        )            where a common radar operating wavelength of λ=0.86 cm has been used. If the radar pulse repetition frequency (PRF) is 40 kHz and the coherent processing interval (CPI) consists of 512 pulses, the resulting Doppler resolution is 78 Hz (≈40 kHz/512), which means that all of the returns from stationary objects in the main beam, including the target, fall into a single Doppler bin. In this geometry, it is not possible to use Doppler processing to achieve fine cross-range resolution.
Due to lack of Doppler resolution, on-target azimuth and elevation angles must be determined from spatial degrees of freedom. However, given a small antenna aperture with a small number of channels of data (spatial degrees of freedom), obtaining accurate angle estimates is a difficult task as well. A simple but accurate approximation to an antenna's 3-dB beamwidth in a particular plane is to take the ratio of the radar's operating wavelength to the length of the antenna in that plane. For a radar seeker, the antenna aperture is usually circular, so the antenna beamwidth in any plane can be approximated as
                              BW                      3            ⁢            d            ⁢                                                  ⁢            B                          ≈                  λ          D                                    (        2        )            where D is the antenna's diameter. For a 6-inch weapon operating at Ka band, the resulting 3-dB beamwidth is ˜0.056 radians or ˜3.2 degrees. Furthermore, the antenna's 3-dB beamwidth can be considered a measure of its Rayleigh or correlation-based resolution. At the beginning of the terminal phase at approximately 3 km from the target, the resulting spatial resolution isδBW≈R·BW3dB=168 m.  (3)Even when the sensor reaches a range of 1.5 km, the resolution is still 84 m. Herein lies the difficulty with real-aperture imaging—the beam limited resolution is proportional to target range, which results in poor cross-range resolution in the radar far field. As the weapon closes on the target, then resolution improves, but by the time individual scattering centers on the target can be resolved, it is too late to adjust course. Therefore, it is imperative to exploit angle estimation or imaging techniques that are more sophisticated than traditional antenna beamforming. Because of the geometry and small antenna aperture, high range resolution is available, but (as described above) angle and Doppler resolution are poor. Thus, an on-target aimpoint must be determined from limited spatial degrees of freedom via monopulse measurement or super-resolution techniques such as maximum likelihood (ML), MUSIC, ESPRIT, or beamforming.
The most common approach is to use some sort of monopulse technique for the target of interest. However, as the weapon approaches a target, the “glint” phenomenon (also known as angular noise) caused by the changing coherence of the scatterers gives rise to rapidly changing signal responses (scintillation). Given a four-channel antenna, we define A, B, C, and D as the measurements taken at the same time instant across the four channel quadrants. Let Σ=A+B+C+D be the sum channel complex signal (V) and Δθ be the delta channel complex signal (V). The delta channel is either Δθ=A+B−(C+D) or Δθ=A+C−(B+D) depending on the desired plane of the angle estimate. Given a sum channel value and a delta channel value, a monopulse angle estimate can be formed as either
                              θ          ^                =                              1                          k              m                                ⁢                      Re            ⁡                          (                                                Δ                  θ                                ∑                            )                                                          (        4        )                                          θ          ^                =                              1            kd                    ⁢                                    tan                              -                1                                      ⁡                          (                                                -                  j                                ⁢                                                      Δ                    θ                                    ∑                                            )                                                          (        5        )            where km is an antenna-dependent monopulse slope factor.
Aimpoint localization performance via monopulse techniques is severely limited by the efficacy of glint mitigation. Another limiting factor of monopulse is that it provides only one angle estimate. The angle estimate may successfully latch onto a dominant scatterer as desired or may latch onto a centroid of multiple scatters or an estimate that lies outside of the target frame. Unfortunately, there is no easy method for detecting or predicting when this detrimental scenario has occurred.
Other super-resolution techniques such as MUSIC, ESPRIT, maximum likelihood, and others are severely limited by the number of signals they are able to detect, require large apertures with many channels, have trouble resolving closely spaced or highly correlated signals, and/or require large sets of training data. In general a single-pulse representation of a signal measured across the antenna array at a particular instant in time can be modeled as a linear combination of spatial basis functions according to
                              x          ⁡                      (            z            )                          =                              ∑            k                    ⁢                                    σ              k                        ⁢                                          α                k                            ⁡                              (                z                )                                                                        (        6        )            where x(z) is the signal to be reconstructed along the spatial coordinate z, Δk(z) is the spatial basis function corresponding to the kth source, and the σk's are the signal/source coefficients. A sampled signal (sampled at particular points in space by the antenna) can be expressed in matrix-vector notation asx=As+n  (7)where the matrix A has basis vectors (sampled versions of αk (z)) as its columns, the column-vector s contains the signal coefficients, and the vector n is the noise introduced to the measurement.
Approaches such as MUSIC and maximum likelihood use covariance-based methods to resolve multiple signals. They take multiple samples of x over time to compute a sample covariance matrix as:R=E[xxH].  (8)MUSIC then searches for basis functions (in this case the antenna steering vectors) that are orthogonal to the noise-only subspace of R. If a basis function (steering vector) is orthogonal to the noise subspace, then it is assumed that this steering vector points to a signal (i.e. a nonzero signal coefficient σk has been found. Maximum likelihood methods perform a brute-force search for the combination of basis functions (steering vectors) that best explain the sample covariance matrix. In both cases, it is necessary to detect the number of sources (i.e., scattering centers) present in the data, and incorrectly detecting the number of sources can affect performance significantly. Furthermore, it takes time to properly train the required covariance matrix, which is a problem in this application because the geometry can change during the training period.